Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

Study of flame-retardant finishing of cellulose fibres: Organic–inorganic hybrid versus conventional organophosphonate

The aim of this study was to introduce a non-formaldehyde inorganic–organic hybrid sol–gel flame-retardant precursor (SiOP) containing phosphorous, nitrogen, and silicon and to compare its functional properties with those of the conventional formaldehyde-containing organic flame-retardant agent, organophosphonate (OP). SiOP was used at concentrations of 2%, 4%, and 8%, and OP was used at a concentration of 200 g/dm³. Both agents were applied to 100% cotton (CO) woven fabric by the pad-dry-cure method under the appropriate conditions. The presence of the SiOP and OP coatings on the CO fabric was confirmed by scanning electron microscopy, energy dispersive X-ray spectroscopy and Fourier-transform infrared spectroscopy. The results of the vertical tests of flammability and the thermogravimetric analyses showed that the presence of the SiOP coating changed the thermal degradation pathway of the CO fabric and resulted in an increase in the thermo-oxidative stability of the cellulose fibres. The thermo-oxidative stability was enhanced by the addition of higher amount of dry solids. At comparable dry solids contents, OP preserved significantly greater flame retardancy and thermo-oxidative stability than did SiOP. These results indicated that the SiOP precursor could not act as an effective alternative to the OP agent in the flame-retardant protection of CO fabric.     

On the signal degradation induced by the interpolation and the sampling rate reduction in aeroacoustics hybrid methods

Taking place within more extensive work that focuses on hybrid methods in aeroacoustics, the present study is devoted to the data transfer operations that are to be performed between two stages of a hybrid calculation. More precisely, the article focuses on two typical operations that usually accompany such data transfer, which are (i) the sampling rate reduction and (ii) the interpolation of the unsteady perturbations to be transmitted from one stage to the other. First part of the paper analyzes the two main issues of such operations, which are the spuriousing and the aliasing phenomena. For doing so, the usual notions of the interpolation theory are revisited before they are synthesized within an original approach. The here proposed formalism allows to understand better both the spuriousing and the aliasing phenomena, as well as to accurately predict the impact of the latter on the data to be transmitted in terms of signal degradation. Second part of the paper provides an illustration and a validation of these theoretical developments via a direct application to a typical aerodynamic noise problem (aeroacoustic emission by a 2D cylinder cross flow). There, it is further shown how the here proposed formalism can help in improving aeroacoustics hybrid calculations by predicting (and thus possibly minimizing) the bias to be induced on the acoustic extrapolation stage because of the aliasing and/or spuriousing effects inherited from the sampling rate reduction and/or interpolation of CFD data—which is likely to occur in any hybrid scenario. Copyright © 2012 John Wiley & Sons, Ltd.     

Zn[aminoacid]2 hybrid materials applied as heterogeneous catalysts in the synthesis of β-enaminones

Hybrid materials have seized attention from scientific community mainly as heterogenic catalysts in organic reactions on a large scale succeeding in some organic compounds with high yields. One of the most important classes of hybrid materials used for this purpose involves the complexation of Zn and aminoacids. Herein, we introduced Zn[Pro]₂ and Zn[Gly]₂ in the synthesis of several β-enaminones via solvent free protocol and using an ultrasound device.     

A Novel Solid‐state Electrochemiluminescent Enantioselective Sensor for Ascorbic Acid and Isoascorbic Acid

A novel, stable, solid‐state and stereoselective electrochemiluminescence (ECL) sensor has been designed to enantioselectively discriminate ascorbic acid (AA) and isoascorbic acid (IAA) by immobilizing Ru(bpy)₃²⁺ (Ru), thiolated β‐cyclodextrin (β‐CD‐SH) and gold/platinum hybrid nanoparticles supported on multiwalled carbon nanotube/silica coaxial nanocables (GP‐CSCN) on glassy carbon electrode. All chemical compounds could be immobilized on the surface of electrode stably through nafion film, and high stereoselectivity could be introduced to the sensor via the synergistic effects of the β‐CD‐SH and GP‐CSCN nanomaterials. When the developed sensor interacted with AA and IAA, obvious difference of ECL intensities was observed, and a larger intensity was obtained from AA, which indicated that this strategy could be employed to enantioselectively recognize AA and IAA. As a result, ECL technique might act as a promising method for recognition of chiral compounds.     

A systematic methodology to design silica templates: Silica microemulsion formulation and nanodroplet type and size estimation

A systematic study of the design and characterization of silica-microemulsion templates is presented. The ternary phase diagrams in micro-heterogeneous systems, by using a non-ionic surfactant (Brij 30) and different silica precursors (MTEOS, TEOS, PTEOS), have been drawn. Based on Khalweit diagrams, the phase inversion temperature was estimated as close to 315 K, for both alchil (TEOS) and aril (PTEOS) types of alcoxides. By correlating the information obtained from phase diagrams at room temperature with that of size effects revealed by VIS absorption molecular probes (bromthymol blue dye), the phase inversion point, i.e. the transition point from water-in-oil to oil-in-water microemulsion, was also clearly established as corresponding to R ∼ 1. Besides technically attractive features such as a wide variety of inorganic and hybrid nanomaterials, high specific surface and highly efficient applicative properties of the final materials, the approach of silica-microemulsion-based templates can be seen as a route towards the Green Chemistry concept.     

Aliphatic Polyester/polyhedral Oligomeric Silsesquioxanes Hybrid Networks via Copper‐free 1,3‐dipolar Cycloaddition Click Reaction

In this study, we describe the preparation and characterization of a new class of thermoset hybrid networks containing aliphatic polyester and polyhedral oligomeric silsesquioxanes (POSS). The copper‐free 1,3‐dipolar cycloaddition click reaction of internal alkyne functionalized aliphatic polyester and multifunctional azido POSS with different concentrations led to highly crosslinked thermoset networks. The click reactions performed under ambient conditions (i.e., in tetrahydrofuran at room temperature for 1 day) in the absence of any catalyst. The chemical composition of hybrid networks and homogenous distribution of POSS molecules were confirmed by Fourier transform infrared spectroscopy and scanning electron microscopy with energy dispersive spectroscopy. The swelling ratios of hybrid networks were commonly decreased by increasing POSS‐N₃ content and by changing polar solvents to apolar solvents. Thermogravimetric analysis results demonstrated that the thermal stability of hybrid networks increased with higher POSS feeding ratio. Tensile tests were applied to evaluate the mechanical properties of hybrid networks. Compared to neat aliphatic polyester, the mechanical properties of hybrid networks significantly improved. For instance, the tensile strength were enhanced from 5 MPa to 19 MPa by increasing the concentration of azido functionalized POSS from 10 to 40. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2222–2227